CN110011749B - Physical layer secure communication method based on sound wave destructive interference in multi-carrier modulation - Google Patents
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Abstract
The invention discloses a physical layer secure communication method based on sound wave destructive interference in multi-carrier modulation, which comprises the following steps: constructing a track equation consisting of points with equal phase difference generated by two fixed sound sources in a plane, converting the track equation into a standard equation of hyperbolas, and determining the number of the sound wave destructive interference hyperbolas; defining a communication safety region by using the wave path difference epsilon; determining the frequency distribution of the sub-carriers by using the fixed wave path difference E; the fixed sub-carrier wave interval analyzes the distribution of the wave path difference epsilon; the power of signal leakage in a destructive interference area is analyzed by utilizing the frequency and wave path difference distribution characteristics of the subcarrier, the artificial noise is added at the receiving end to cover the signal power of the signal leakage in a safety area after destructive interference at the sending end, the receiving end demodulates the signal after removing the artificial noise from the received signal, and an eavesdropper is unknown to the artificial noise and cannot remove the noise to acquire the signal. The invention constructs a communication safety region based on multi-carrier modulation according to the destructive interference principle of sound waves, and improves the data transmission safety.
Description
Technical Field
The invention relates to the field of wireless communication, in particular to a physical layer secure communication method based on sound wave destructive interference in multi-carrier modulation.
Background
With the development of Acoustic Near Field Communication (a-NFC) technology in recent years, the technology has rapidly become widespread and applied in the fields of mobile payment, device connection, smart home and the like. The sound wave near field communication technology can perform data communication with small data volume, such as transmission of payment user ID, equipment handshake connection and the like, and can replace application of partial two-dimensional codes. The sound wave near field communication technology does not need to open complicated operations such as App code scanning and camera focusing like a two-dimensional code, and overcomes the fatal defect that the two-dimensional code cannot be scanned after being artificially damaged.
The existing acoustic wave NFC technology applied to the market does not take data transmission safety into consideration, and transmitted data are information which does not need to be encrypted, such as a link, a user ID and the like. This greatly limits the application scenarios of acoustic NFC.
Due to the limitation of the hardware characteristics of the microphone and the loudspeaker, the bandwidth available for the sound wave near field communication is very small, and the requirement on real-time performance is high, so that the method based on the traditional secret key encryption is not suitable. With the increasing use of double loudspeakers of intelligent terminals in recent years, the invention provides a physical layer secure communication method based on sound wave destructive interference, which comprises the following steps: based on multi-carrier modulation, the two loudspeakers are used for simultaneously sending the same signals, and the frequency intervals of subcarriers are designed according to the destructive interference principle of sound waves, so that a destructive interference area is seamlessly spliced in space, an eavesdropper can not always receive some subcarriers at any point in free space, effective information can not be acquired, and safe transmission of data is realized.
Disclosure of Invention
The invention provides a method for overcoming the defect of insufficient data transmission safety in the existing sound wave near field communication.
The present invention aims to solve the above technical problem at least to some extent.
The primary objective of the present invention is to solve the above technical problems, and the technical solution of the present invention is as follows:
a method of physical layer secure communication based on acoustic wave destructive interference in multi-carrier modulation, the method comprising:
s1: constructing a track equation consisting of points with equal phase difference generated by two fixed sound sources in a plane, forming the track equation into a standard equation of hyperbolas according to the definition of sound wave destructive interference, and simultaneously determining the number of the sound wave destructive interference hyperbolas;
s2: defining a communication safety region by utilizing a set wave path difference epsilon in a destructive interference hyperbola;
s3: fixing the wave path difference epsilon, and confirming the frequency distribution of the neutron carrier wave in the destructive interference hyperbola;
s4: the distribution of wave path differences epsilon is analyzed in the interval of the subcarriers in the fixed destructive interference hyperbola;
s5: and (4) analyzing the power of signal leakage in the destructive interference region by using the frequency distribution characteristics and the wave path difference distribution characteristics of the subcarrier distribution in the step (S3) and the step (S4), adding artificial noise into the transmitted signal to cover the power of the leaked signal, and demodulating the signal by removing the known artificial noise from the received signal at the receiving end.
Further, the trajectory equation formed by the points with equal phase difference generated by the two fixed sound sources in the plane is as follows:
where c is the coordinate of the two fixed sound sources on the X-axis, λ is the wavelength, v0The speed of sound wave propagation in the air is 340m/s, f is the frequency of the current carrier wave, k is a real number and represents a wave path difference factor, interference cancellation is performed when k is odd, and interference expansion is performed when k is even;
the standard equation of the hyperbola is as follows:
wherein,
further, in the acoustic near field communication, when the maximum value of f is 22050, and c is 1, the upper limit of k is 259.411, and at this time, the number N of destructive interference hyperbolas is 129, and the number of subcarriers should be N-th power of 2 based on the multicarrier modulation requirement of the fast fourier transform, and N is 128.
Further, when the wave path difference is E, the communication safety area is
k is the wave path difference factor, k is odd number, and lambda is the wavelength. The power of the carrier frequency signal in the communication safety area is smaller, if the communication channel has noise, and the noise power is higher than the signal power of the communication safety areaAnd the signal-to-noise ratio is less than 0dB, and the eavesdropper cannot demodulate the signal. In multi-carrier communication, N communication safety areas are seamlessly spliced together to form a large communication safety area in the whole space by changing the frequency of N carriers.
Further, the fixed wave path difference epsilon, and the frequency distribution of the neutron carrier wave in the destructive interference hyperbola is as follows:
uniformly dividing the area between the first and second destructive interference hyperbolas on the same side of Y axis into n parts according to the wave path difference, and setting the 1 st subcarrier frequency as f1Frequency f of ith subcarrieriThe following relationships exist:
Wherein λ isiThe wavelength of the ith sub-carrier is sorted out
The number of destructive interference hyperbolas is set to N, and the ith subcarrier frequency between the jth destructive interference hyperbola and the j +1 th destructive interference hyperbola is represented as fjiThen the expression is:
wherein, the value range of i is an integer between 1 and n; n interference cancellation hyperbolas are total in the communication frequency band, and the value range of j is an integer between 1 and N-1; f. of(j-1)8The frequency of the last communications safe area of the last destructive interference hyperbola.
Further, the subcarrier spacing is set to a fixed value Δ f, and the number of subcarriers N, N is 2nThe point where the destructive interference hyperbola intersects the X axis is
Where k is an odd number, k is a wave path difference factor, v0For the speed of sound wave propagation in air being 340m/s, f being the frequency of current carrier wave, according to the principle of destructive interference zone splicing, the destructive interference line of the ith subcarrier passes through epsiloniIs exactly the destructive interference line of the (i + 1) th subcarrier, so there is:
wherein λ isiFor the wavelength of the ith subcarrier, the simplified wave path difference E belongs toiIs represented as follows:
wherein i ═ 1, 2, 3. The intervals of the multicarrier modulation subcarriers based on the fast fourier transform are fixed and thus it is necessary to confirm the distribution of the path difference at the fixed subcarrier intervals.
Further, due to the existence of the wave path difference epsilon, complete interference cancellation cannot be realized, signal power leakage exists in a destructive interference area, a point P is set to be a position of destructive interference, and the amplitudes of sine waves emitted by two fixed sound sources are S respectively1And S2，
And
respectively, the phase difference is S, the amplitude is P and the combined signal at the point P is S
r1And r2And respectively represent the distances, r, from two fixed sound sources to the point P2-r1Is the difference in the path of two fixed sources to the P point:
if two fixed sound sources send sine waves with the same unit amplitude and initial phase, then
Will be provided with
Bringing in
Obtaining:
the average power of the signal at point P is therefore:
adding artificial noise into a signal sent by a sending end, wherein the artificial noise is Gaussian white noise, and the average power of the Gaussian white noise is greater than the average power P of the signalavg。
Further, in the sound wave near field communication, the transmitting power of the transmitting end is P0Self-interference noise e at the receiving endjIs Gaussian white noise, and the average power of the self-interference noise is
Background noise e of the surroundingsnIs white Gaussian noise, and the average power of the background noise is
Setting a channel gain h from a sender to a receivertThe channel gain from the sender to the eavesdropper is gtThe receiver-to-eavesdropper channel gain is hbeReceiver self-interference channel gain of hbbWith the receiver's channel output of Y and the eavesdropper's channel output of Z, at time t, x is transmitted for the transmitted signaltY and Z have the following relationships:
at an average power P0With the constraint of (2), the secrecy capacity C of the acoustic near field communication transmission systemsComprises the following steps:
the secret capacity analysis of the acoustic wave near field communication transmission system when the fixed wave path difference belongs to the field is as follows:
setting the epsilon as 1/8 wave length, when the eavesdropper is at any position P in the secret area and the transmitting power of each double loudspeaker at the transmitting end is unit power, the average power P of 8 sub-carriers within one wave distance difference1Comprises the following steps:
the average power of the integral wave path differences at P is P1The receiver is in the middle of the transmitter's double microphones and always in the interference range overlapping area, the signal power at the receiver's receiving end is 2, the system secrecy capacity receiver's end is self-interference noise ejThe relationship of (1) is:
the secret capacity analysis of the acoustic wave near field communication transmission system at fixed subcarrier spacing is as follows:
when the highest subcarrier frequency is 20000Hz and the subcarrier spacing is equal, there are N subcarriers between 20-20kHz, and the average power of all subcarriers at any point in the communication security region is:
compared with the prior art, the technical scheme of the invention has the beneficial effects that:
the invention is based on multicarrier modulation to send the same signal through two fixed sound sources at the sending end of near field communication, and designs the frequency interval of the subcarrier according to the destructive interference principle of the sound wave, so that the destructive interference area is seamlessly spliced in the space, and an eavesdropper always has the subcarrier not to receive at any point in the free space, thereby being incapable of demodulating effective information and ensuring the safety of data transmission.
Drawings
FIG. 1 is a schematic diagram of acoustic wave interference.
FIG. 2 is a schematic illustration of the splicing of the acoustic wave destructive interference zones.
Fig. 3 is a frequency distribution diagram of subcarriers when the path difference e is 1/8 wavelengths.
Fig. 4 is a graph of the distribution of the safety region of communication in space when the path difference e is 1/8 wavelengths.
Fig. 5 is a distribution diagram of the path difference e between the subcarriers when the number N of subcarriers is 128.
FIG. 6 is a graph showing the variation of signal leakage power according to E at any point in space.
Fig. 7 is a schematic diagram of a physical layer security method based on the combination of sound wave destructive interference and artificial noise.
FIG. 8 is a graph of system privacy capacity as a function of Bob-side self-interference power.
Fig. 9 is a diagram showing the relationship between the system security capacity and the self-interference noise power under different numbers of subcarriers.
Detailed Description
The technical solution of the present invention is further described below with reference to the accompanying drawings and examples.
Example 1
As shown in fig. 1, a method for physical layer secure communication based on sound wave destructive interference in multi-carrier modulation, the method comprising:
s1: constructing a track equation consisting of points with equal phase difference generated by two fixed sound sources in a plane, forming the track equation into a standard equation of hyperbolas according to the definition of sound wave destructive interference, and simultaneously determining the number of the sound wave destructive interference hyperbolas;
in this embodiment, as shown in fig. 1, a schematic diagram of acoustic wave interference is shown, and a trajectory equation formed by points with equal phase difference generated in a plane by two fixed sound sources is as follows:
where c is the coordinate of the two fixed sound sources on the X-axis, λ is the wavelength, v0The speed of sound wave propagation in the air is 340m/s, f is the frequency of the current carrier wave, k is a real number and represents a wave path difference factor, interference cancellation is performed when k is odd, and interference expansion is performed when k is even;
the standard equation of the hyperbola is as follows:
wherein,
in the acoustic near field communication, the maximum value of f is 22050, when c is 1, the upper limit of k is 259.411, the number N of destructive interference hyperbolas is 129, and when the requirement of multicarrier modulation by fast fourier transform is satisfied, the number of subcarriers should be N-th power of 2, and N is 128.
S2: defining a communication safety region by utilizing a set wave path difference epsilon in a destructive interference hyperbola;
when the wave path difference is E, the communication safety area is
k is the wave path difference factor, k is odd number, and lambda is the wavelength. In the invention, the power of the carrier frequency signal in the communication safety area is smaller, if the communication channel has noise and the noise power is higher than the signal power of the communication safety area, the signal-to-noise ratio is less than 0dB, and the eavesdropper cannot demodulate the signal. In multi-carrier communication, by changing the frequency of N carriers, the N communication safety areas are seamlessly spliced to form a large communication safety area in the whole space. Such as the splicing schematic diagram of the acoustic wave destructive interference region in fig. 2.
S3: fixing the wave path difference epsilon, and confirming the frequency distribution of the neutron carrier wave in the destructive interference hyperbola;
in this embodiment, the fixed wave path difference e is as follows, and the frequency distribution of the neutron carrier wave in the destructive interference hyperbolic curve is as follows:
uniformly dividing the area between the first and second destructive interference hyperbolas on the same side of Y axis into n parts according to the wave path difference, and setting the 1 st subcarrier frequency as f1Frequency f of ith subcarrieriThe following relationships exist:
Wherein，λiThe wavelength of the ith sub-carrier is sorted out
The number of destructive interference hyperbolas is set to N, and the ith subcarrier frequency between the jth destructive interference hyperbola and the j +1 th destructive interference hyperbola is represented as fjiThen the expression is:
wherein, the value range of i is an integer between 1 and n; n interference cancellation hyperbolas are total in the communication frequency band, and the value range of j is an integer between 1 and N-1; f. of(j-1)8The frequency of the last communications safe area of the last destructive interference hyperbola.
In a sound wave near field communication scene, when a frequency range is within an audio frequency band of 20-20000Hz, and a wave path difference e is 1/8 wavelengths (that is, n is 8), each subcarrier frequency distribution is as shown in fig. 3, an operating frequency band is between 20-20000Hz, the frequency band is divided into 7 groups of destructive interference hyperbolas, and each group is formed by splicing 8 destructive interference regions. Since the frequency of the 50 th sub-carrier is 20.6146Hz, and the frequency of the 51 st sub-carrier is 17.2840<20Hz, only 50 sub-carriers are needed to seamlessly splice into communication safety regions in a plane. As shown in fig. 4, the distribution diagram of the safety region of communication in space when the wave path difference e is 1/8 wavelengths.
S4: the distribution of wave path differences epsilon is analyzed in the interval of the subcarriers in the fixed destructive interference hyperbola;
setting the subcarrier spacing as a fixed value delta f, and the number of subcarriers N, N being 2nThe point where the destructive interference hyperbola intersects the X axis is
Where k is an odd number, k is a wave path difference factor, v0The speed of sound wave propagating in the air is 340m/s, f is the frequency of the current carrier wave, and the ith subcarrier wave is spliced according to the principle of destructive interference regionPassing through the destructive interference lineiIs exactly the destructive interference line of the (i + 1) th subcarrier, so there is:
wherein λ isiFor the wavelength of the ith subcarrier, the simplified wave path difference E belongs toiIs represented as follows:
wherein i ═ 1, 2, 3. The intervals of the FFT-based multicarrier modulation subcarriers are fixed and thus it is necessary to confirm the distribution of the path difference at the fixed subcarrier intervals. When N is 128, the wave path difference between each subcarrier is epsiloniThe distribution of (c) is shown in fig. 5.
Taking an audio frequency band of 20-20000Hz for sound wave incoming communication as an example, the sub-frequency band is evenly divided into N parts, and each sub-carrier frequency interval is the same. Let e beiLess than 1/8 wavelengths is reasonable. Then when the total number of N is greater than 8, there are always 8 subcarriers with the lowest frequency that do not meet the requirements. Therefore, in this case, the 8 subcarriers with the lowest frequency should be discarded during the communication process, and other subcarriers should be used to transmit information.
S5: and (4) analyzing the power of signal leakage in the destructive interference region by using the frequency distribution characteristics and the wave path difference distribution characteristics of the subcarrier distribution in the step (S3) and the step (S4), adding artificial noise into the transmitted signal to cover the power of the leaked signal, and demodulating the signal by removing the known artificial noise from the received signal at the receiving end.
In this embodiment, due to the existence of the wave path difference e, complete interference cancellation cannot be performed, signal power leakage exists in the destructive interference region, the point P is set as one position of the interference cancellation, and the amplitudes of the sine waves emitted by the two fixed sound sources are respectively S1And S2，
And
respectively, the phase difference is S, the amplitude is P and the combined signal at the point P is S
r1And r2And respectively represent the distances, r, from two fixed sound sources to the point P2-r1Is the difference in the path of two fixed sources to the P point:
if two fixed sound sources send sine waves with the same unit amplitude and initial phase, then
Will be provided with
Bringing in
Obtaining:
the average power of the signal at point P is therefore:
adding artificial noise into a signal sent by a sending end, wherein the artificial noise is Gaussian white noise, and the average power of the Gaussian white noise is greater than the average power P of the signalavgAnd the signal-to-noise ratio in the safety area is less than 0dB, so that an eavesdropper cannot effectively demodulate the signal. Fig. 6 shows a graph of the variation of the signal leakage power according to e at any point in space. Fig. 7 shows a schematic diagram of a physical layer security method based on the combination of sound wave destructive interference and artificial noise.
In this embodiment, in a sound wave near field communication scenario, the transmission power of the transmitting end is P0Limited, self-interference noise e at the receiving endjIs Gaussian white noise, and the average power of the self-interference noise is
Background noise e of the surroundingsnIs white Gaussian noise, and the average power of the background noise is
Setting a channel gain h from a sender to a receivertThe channel gain from the sender to the eavesdropper is htThe receiver-to-eavesdropper channel gain is hbeReceiver self-interference channel gain of hbbWith the receiver's channel output of Y and the eavesdropper's channel output of Z, at time t, x is transmitted for the transmitted signaltY and Z have the following relationships:
at an average power P0With the constraint of (2), the secrecy capacity C of the acoustic near field communication transmission systemsComprises the following steps:
the secret capacity analysis of the acoustic wave near field communication transmission system when the fixed wave path difference belongs to the field is as follows:
setting the epsilon as 1/8 wave length, when the eavesdropper is at any position P in the secret area and the transmitting power of each double loudspeaker at the transmitting end is unit power, the average power P of 8 sub-carriers within one wave distance difference1Comprises the following steps:
the average power of the integral wave path differences at P is P1The receiver is positioned in the middle of the double microphones of the sender and always positioned in the interference amplitude superposition area, the signal power of the receiving end of the receiver is 2, the secret capacity of the sound wave near field communication transmission system and the self-interference noise e of the receiving end of the receiverjThe relationship of (1) is:
make the background of the surrounding environment Gaussian white noise ejOf (2) is
After the numerical simulation calculation, as shown in fig. 8. When the total transmitting power of the sender is 1, under the same interference noise power, the system safety capacity is higher based on the destructive interference method, or on the premise of reaching the same confidentiality capacity, the destructive interference method needs the sender to transmitThe artificial noise power is lower. When the total transmitting power of a sender is 2, the system has higher system safety capacity based on a destructive interference method; in addition, under the same interference noise power, when the transmitting power of the transmitter is 1, the method based on destructive interference can obtain the same safe capacity as that when the transmitting power of the transmitter is 2.
The transmission system at fixed subcarrier spacing was analyzed for its privacy capacity as follows:
when the highest subcarrier frequency is 20000Hz and the subcarrier spacing is equal, there are N subcarriers between 20-20kHz, and the average power of all subcarriers at any point in the communication security region is:
as can be seen from fig. 9, under the limitation of the acoustic near-field communication bandwidth, as the value of N, the security capacity of the acoustic near-field communication transmission system increases to approach the limit relatively quickly, but no matter how much N increases, the security capacity of the system does not exceed the upper limit. When the transmitting power is the same and the subcarrier interval is fixed, the method of the invention needs lower self-interference noise power of the Bob terminal than the traditional self-interference elimination method under the same secret capacity; the method has higher security capacity than the traditional self-interference elimination method under the condition of the same self-interference noise power.
The same or similar reference numerals correspond to the same or similar parts;
the terms describing positional relationships in the drawings are for illustrative purposes only and are not to be construed as limiting the patent;
it should be understood that the above-described embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And are neither required nor exhaustive of all embodiments. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the protection scope of the claims of the present invention.
Claims (4)
1. A method for physical layer secure communication based on acoustic wave destructive interference in multi-carrier modulation, the method comprising:
s1: constructing a track equation consisting of points with equal phase difference generated by two fixed sound sources in a plane, forming the track equation into a standard equation of hyperbolas according to the definition of sound wave destructive interference, and simultaneously determining the number of the sound wave destructive interference hyperbolas;
s2: defining a communication safety area by using a set wave path difference E in a destructive interference hyperbola, and when the wave path difference E is within the range, the communication safety area is
k is a wave path difference factor, k is an odd number, and lambda is a wavelength;
s3: fixing the wave path difference epsilon, and confirming the frequency distribution of the neutron carrier wave in the destructive interference hyperbola;
the fixed wave path difference is epsilon, and the frequency distribution of the neutron carrier wave in the destructive interference hyperbola is as follows:
uniformly dividing the area between the first and second destructive interference hyperbolas on the same side of Y axis into n parts according to the wave path difference, and setting the 1 st subcarrier frequency as f1Frequency f of ith subcarrieriThe following relationships exist:
Wherein λ isiThe wavelength of the ith sub-carrier is sorted out
The number of destructive interference hyperbolas is set to N, and the ith subcarrier frequency between the jth destructive interference hyperbola and the j +1 th destructive interference hyperbola is represented as fjiThen the expression is:
wherein, the value range of i is an integer between 1 and n; n interference cancellation hyperbolas are total in the communication frequency band, and the value range of j is an integer between 1 and N-1; f. of(j-1)8The frequency of the last communications safe area of the last destructive interference hyperbola;
s4: the distribution of wave path differences epsilon is analyzed in the interval of the subcarriers in the fixed destructive interference hyperbola;
setting the subcarrier spacing as a fixed value delta f, and the number of subcarriers N, N being 2nThe point where the destructive interference hyperbola intersects the X axis is
Where k is an odd number, k is a wave path difference factor, v0The speed of sound wave propagating in the air is 340m/s, f is the frequency of the current carrier wave, lambda is the wavelength, according to the principle of destructive interference region splicing, the destructive interference line of the ith subcarrier passes through epsiloniIs exactly the destructive interference line of the (i + 1) th subcarrier, so there is:
wherein λ isiFor the wavelength of the ith subcarrier, the simplified wave path difference E belongs toiIs represented as follows:
wherein i ═ 1, 2, 3.. N-1;
s5: analyzing the power of signal leakage in the destructive interference region by using the frequency distribution characteristics and the wave path difference distribution characteristics of the subcarrier distribution in the steps S3 and S4, adding artificial noise into the transmitted signal to cover the power of the leaked signal, and demodulating the signal by the receiving end after removing the known artificial noise from the received signal;
signal power leakage exists in a destructive interference area, a P point is set to be a destructive interference position, and amplitudes of sine waves emitted by two fixed sound sources are S respectively1And S2，
And
respectively, the phase difference is S, the amplitude is P and the combined signal at the point P is S
r1And r2And respectively represent the distances, r, from two fixed sound sources to the point P2-r1Is the difference in the path of two fixed sources to the P point:
if two fixed sound sources send sine waves with the same unit amplitude and initial phase, then
Will be provided with
Bringing in
Obtaining:
the average power of the signal at point P is therefore:
adding artificial noise into a signal sent by a sending end, wherein the artificial noise is Gaussian white noise, and the average power of the Gaussian white noise is greater than the average power P of the signal sentavg。
2. The method for physical layer secure communication based on acoustic wave destructive interference in multi-carrier modulation according to claim 1, wherein the trajectory equation of the points of equal phase difference generated by the two fixed acoustic sources in the plane is as follows:
where c is the coordinate of the two fixed sound sources on the X-axis, λ is the wavelength, v0The speed of sound wave propagation in the air is 340m/s, f is the frequency of the current carrier wave, k is a real number and represents a wave path difference factor, interference cancellation is performed when k is odd, and interference expansion is performed when k is even;
the standard equation of the hyperbola is as follows:
wherein,
3. the physical layer security communication method based on sound wave destructive interference in multi-carrier modulation as claimed in claim 2, wherein in sound wave near field communication, the maximum value of f is 22050, c is set to 1, the upper limit of k is 259.411, the number of destructive interference hyperbolas N is k/2 to 129, and N is 128 when the number of subcarriers is N powers of 2 based on the requirement of fast fourier transform multi-carrier modulation.
4. The physical layer security communication method based on sound wave destructive interference in multi-carrier modulation as claimed in claim 1, wherein in the sound wave near field communication, the transmission power of the transmitting end is P0Self-interference noise e at the receiving endjIs Gaussian white noise, and the average power of the self-interference noise is
Background noise e of the surroundingsnIs white Gaussian noise, and the average power of the background noise is
Setting a channel gain h from a sender to a receivertThe channel gain from the sender to the eavesdropper is gtThe receiver-to-eavesdropper channel gain is hbeReceiver self-interference channel gain of hbbWith the receiver's channel output of Y and the eavesdropper's channel output of Z, at time t, x is transmitted for the transmitted signaltY and Z have the following relationships:
at an average power P0With the constraint of (2), the secrecy capacity C of the acoustic near field communication transmission systemsComprises the following steps:
the secret capacity analysis of the acoustic wave near field communication transmission system when the fixed wave path difference belongs to the field is as follows:
setting the epsilon as 1/8 wave length, when the eavesdropper is at any position P in the secret area and the transmitting power of each double loudspeaker at the transmitting end is unit power, the average power P of 8 sub-carriers within one wave distance difference1Comprises the following steps:
the average power of the integral wave path differences at P is P1The receiver is positioned in the middle of the double microphones of the sender and always positioned in the interference amplitude superposition area, the signal power of the receiving end of the receiver is 2, the secret capacity of the sound wave near field communication transmission system and the self-interference noise e of the receiving end of the receiverjThe relationship of (1) is:
the secret capacity analysis of the acoustic wave near field communication transmission system at fixed subcarrier spacing is as follows:
when the highest subcarrier frequency is 20000Hz and the subcarrier spacing is equal, there are N subcarriers between 20-20kHz, and the average power of all subcarriers at any point in the communication security region is:
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